Math Contests

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Math Contests 2009/2010

• Jeff Soesbe
• Volunteer Math Contest Coordinator
• jeff.soesbe_at_sanjuan.edu

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Agenda

• Why Math Contests?
• Rocket City
• SACMATH
• Mathletes
• MOEMS
• MathCounts
• Math League
• AMC
• Models for Participation
• For Top-Level Students Mandelbrot, USAMTS, ARML

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Why Math Contests?

• Build Problem Solving Skills
• Math can be competitive, and fun!
• Provide a challenge
• A chance to shine
• Uncover hidden gems

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Rocket City Math League

• Grades Middle and High School
• Format
• Tests at different levels
• Pre-Algebra, Algebra-I, Geometry, Algebra-II,
  Pre-Calc (and above)
• Students take the test for the highest math in
  which theyre currently enrolled or have finished
• 3 Individual tests during the year, one
  Interschool (Team) test
• Each Individual Test has 12 questions with
  different point values, total of 25 points. (Team
  test is 15 questions.)
• Cost FREE! FREE! (Funded by Mu Alpha Theta)
• Awards Top scoring individuals and teams
  recognized, nationally and in regions
• Dates Registration opened Sept 14. Monthly tests
  run December through March
• Website www.rocketcitymath.org

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Rocket City Sample Questions

• Explorer (Pre-Algebra)
• The minimum age required to work at Jeromes
  Pizza Dome is 17. Five years ago, Lonan the baker
  was 3 years older than the minimum age. In 2
  years Taj the delivery guy will be 4 years older
  than Lonan is now. How old is Taj now? (3 points)
• Mercury (Algebra-I)
• Six Zorcs, two Ners and three Kerals are better
  at math than three Zorcs, nine Kerals, and two
  Ners. If each alien has the same mathematical
  abilites of all the other aliens in its species
  (all Zorcs are as good as math as all other
  Zorcs), who is better at math, a Zorc or a Keral?
  (2 points)
• Gemini (Geometry)
• A space ship lands in a crop field and leaves a
  crop circle, where the crop will not grow,
  defined by the equation 2x2 2y2 32. The
  farmer that owns the field gets 5 cobs of corn
  for every 2p square units of his crop field. How
  many cobs of corn did the farmer lose after the
  space ship made the circle? (2 points)
• Apollo (Algebra-II)
• Oyo has a list of all of the prime numbers
  between 1 and 100. If he randomly selects 2
  different numbers from the list, what is the
  probability that their sum is even? (2 points)
• Discovery (Pre-Calculus and above)
• Find the sum of all real x that satisfy the
  equation x2 3 3x1. (1 point)

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SACMATH

• Sacramento Area Competitions in Mathematics
• Three Contests
• Elementary School Contest on Sat, Oct 24 at
  Winston Churchill MS
• Middle School Contest on Sat, Nov 14 at Casa
  Roble HS (?)
• High School Contest on Sat, Dec 5 at UC Davis
• Format Individual and Team Tests
• Individual Number Sense, Target, Sprint (all
  levels), Countdown (MS)
• Team Team (all levels) Relay (HS)
• Similar in format to MathCounts, AMC, and ARML
• Registration
• Students register as Teams, or can register as
  Individuals
• Schools/Teachers can organize teams, but not
  required
• Cost 40 for Team (discount for early reg!) or
  10 per Individual
• Help publicize the contest! Volunteers always
  welcome!
• Website www.sacmath.com
• Contact Jeff Soesbe (sacmathcontests_at_gmail.com)

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Mathletes

• Grades High School
• Run by Sacramento City School District
• Both Sierra College and CSUS are also involved
• One Wednesday afternoon per month, after school
• At different host school each month
• Championship in May at Sac State
• Format Four individual subject area tests, one
  problem solving test
• Subject Area Numbers, Algebra, Geometry,
  Trigonometry
• Five students per team each student takes two
  tests
• Schools can bring as many teams as they like (I
  think)
• Want to get SJUSD schools involved!
• Go to SacCity contests? Contact Bill Phillips,
  Sheldon HS (wphillip_at_egusd.net)
• Is there interest in North District contests?
  Contact Jeff or contact Brian Roth at Casa Roble.

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MOEMS

• Grades 4th thru 8th grades
• Format
• 5 monthly tests, each with 5 questions.
• Tests have a time limit for each question (give
  them one by one, or all at once)
• Team score sum of top 10 individual scores
• Two Divisions E (Grade 4 6) M (Grade 7 8)
• Cost 89/99 (email/US mail) for 1 school team
  (up to 35 students)
• Awards Many, for individuals and school teams
• Dates
• Register by Sept 30, tests are Nov Mar.
• Website www.moems.org

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MOEMS Sample Questions

• Division E (Time 5 minutes)
• A grocer bought 15 dozen oranges at 1.00 a
  dozen. She threw away 20 rotten oranges, and then
  sold the rest at 8 oranges for 85 cents. How much
  profit did the grocer make, in dollars and cents?
• Division M (Time 4 minutes)
• Suppose it is now the month of November. What
  month will it be 100 calendar months from now?

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MathCounts

• Grades 6th thru 8th grades
• Format
• Team and individual contests, at different
  levels School, then Chapter, then State, then
  National (top school teams and individuals
  advance to next level)
• Four contests
• Sprint (individual 30 questions, 40 min)
• Target (individual 8 questions, 2 at a time, 6
  min per pair )
• Team (10 questions, 20 minutes)
• Countdown (top individuals, head to head, State
  level and above)
• Club Program for year-long participation
  (Oct-Mar)
• Take 1 Challenge test/month awards based on
  participation and score
• Cost 90 per team (4 people), 25/person for
  extra individual
• Awards Top teams and individuals at each level
• Dates Register by Dec 11, contests are Feb, Mar,
  May.
• Website www.mathcounts.org

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MathCounts Sample Questions

• Sprint 27) The function f is defined by f (n)
  f (n - 1) f (n - 2). It is also true that f (1)
  3 and f (3) 10. What is the value of f (6)?
• Target 5) What is the greatest whole number that
  MUST be a factor of the sum of any four
  consecutive positive odd numbers?
• Team 3) Emma and Ed walk into a room containing
  30 assembled Tworks and enough pieces to assemble
  100 more Tworks. A Twork takes eight minutes to
  assemble and 10 minutes to disassemble. If Emma
  starts assembling Tworks as Ed begins
  disassembling the ones that were already made,
  and they both continue to work until there are
  exactly 35 assembled Tworks in the room (and no
  partially assembled or disassembled Tworks), how
  many minutes will Emma have worked?

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Math League

• Grades 4th through 12th grades
• Format
• Grade 4 8 1 test, 30 mins, 30 or 40
  mult-choice Qs
• High School 6 monthly tests, each 30 mins, with
  6 Qs
• School team score sum of top 5 individual
  scores
• Cost
• Grade 4 8 30 30 tests for 1 grade
• High School 75 30 tests for the year
• Awards Top teams in region and state
• Dates
• Grade 4 - 8 Register by Jan 31, contest in Feb
  (Grades 6 - 8) or April (Grades 4 - 5).
• High School Register by Oct 15, contests are Oct
  Apr.
• Website www.mathleague.com

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Math League Sample Questions

• 4th Grade 11) 8 dozen __?__ X 24 pairs.
• A) 2 B) 4 C) 8 C) 12
• 5th Grade, 24) By playing on the Music Truck,
  more than 4 friends (but fewer than 9) earned a
  total of 88.92. If each got the same pay, how
  much was each paid?
• A) 17.78 B) 14.82 C) 12.70 D) 11.12
• 6th Grade, 14) 25 of one hour __?__ minutes.
• A) 10 B) 12 C) 15 D) 25

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AMC

• Grades 6th through 12th grades
• Format
• Different levels of individual tests, top scorers
  on one test advance to next test
• AMC-8/10/12 (25 Q mult choice, 45/75/75 mins)
• AIME (15 Q with integer answer, 3 hours by
  invitation)
• USAMO (6 essay/proof Q in 9 hours over 2 days by
  invitation)
• IMO (6 person US team invitation only)
• Cost 33-60 dep on grade/date 11-16 for 10
  tests
• Awards Top scorers in school and nationally, top
  teams
• Dates Register by Oct/Dec (AMC8/AMC1012),
  contests are Nov/Feb (AMC8/AMC1012).
• Website www.unl.edu/amc

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AMC Sample Questions

• 2002 AMC-8, 21) Harold tosses a nickel four
  times. The probability that he gets at least as
  many heads as tails is
• (A) 5/16 (B) 3/8 (C) 1/2 (D) 5/8 (E)
  11/16
• 2004 AMC-10, 11 A company sells peanut butter in
  cylindrical jars. Marketing research suggests
  that using wider jars will increase sales. If the
  diameter of the jars is increased by 25 without
  increasing the volume, by what percent must the
  height be decreased?
• (A) 10 (B) 25 (C) 36 (D) 50 (E) 60
• 2004 AMC-12, 3) For how many ordered pairs of
  positive integers (x, y) is x 2y 100?
• (A) 33 (B) 49 (C) 50 (D) 99 (E) 100
• 2003 AIME Practice 1) The product N of three
  positive integers is 6 times their sum, and one
  of the integers is the sum of the other two. Find
  the sum of all possible values of N.

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Models of Participation

• Just Show Up!
• No prep, take the contest
• Math League, MathCounts, AMC, SACMATH
• In-Class Participation
• Rocket City (really good), MOEMS (really good),
  Math League, AMC
• Lunchtime Club
• Rocket City (maybe), MathCounts, Math League,
  AMC, MOEMS (maybe), SACMATH
• Math Contest Club
• Rocket City, MathCounts, MOEMS, Math League, AMC,
  SACMATH

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Contests for Top Level Students

• Mandelbrot Competition
• Grades High School
• Format Seven questions, with different point
  values. Individual and Team tests
• Cost 32
• Awards prizes for top Individuals and School in
  a region and nationally
• Dates Register by Sept 30 (late reg by Oct 31)
  Tests are Nov through Mar
• Website http//www.mandelbrot.org

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Mandelbrot Sample Questions

• (1 point) 1. The sequence 1, x, 6, y is an
  arithmetic progression. Find xy.
• (2 points) 4. The positive integers 30, 72, and N
  have the property that the product of any two of
  them is divisible by the third. What is the
  smallest possible value of N?
• (3 points) 7. A quadrilateral inscribed in a
  circle has side lengths whose squares are 17, 99,
  19, and 97. Find the area of the circle.

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USAMTS

• USA Math Talent Search (USAMTS)
• Grades High School
• Format Five essay proof questions, for four
  rounds
• Cost free
• Awards none
• Dates October through March
• Website http//www.usamts.org

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USAMTS Sample Questions

• 1/1/18. When we perform a digit slide on a
  number, we move its units digit to the front of
  the number. For example, the result of a digit
  slide on 6471 is 1647. What is the smallest
  positive integer with 4 as its units digit such
  that the result of a digit slide on the number
  equals 4 times the number?
• 5/1/18. ABCD is a tetrahedron such that AB 6,
  BC 8, AC AD 10, and BD CD 12. Plane P
  is parallel to face ABC and divides the
  tetrahedron into two pieces of equal volume.
  Plane Q is parallel to face DBC and also divides
  ABCD into two pieces of equal volume. Line L is
  the intersection of planes P and Q. Find the
  length of the portion of L that is inside ABCD.

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ARML

• American Regions Math League
• Grades High School
• Format Regional Teams compete in a nationwide
  contest, held at three sites. Closest site is Las
  Vegas.
• Individual contest
• Team contest
• Power question
• Relay question
• Cost contest and travel to contest site
• Awards teams and individuals in different
  divisions
• Dates June 4-5, 2010
• Website http//www.arml.com
• A team from the area is organized by UC Davis, as
  part of Explore Math program (www.math.ucdavis.edu
  /exploration)
• Contact arml_at_math.ucdavis.edu

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Other Information

• Contact information
• Jeff Soesbe, Volunteer Math Contest Coordinator,
• jeff.soesbe_at_sanjuan.edu